$\dfrac{ 8b - 5c }{ -3 } = \dfrac{ 10b + 9d }{ 2 }$ Solve for $b$.
Answer: Multiply both sides by the left denominator. $\dfrac{ 8b - 5c }{ -{3} } = \dfrac{ 10b + 9d }{ 2 }$ $-{3} \cdot \dfrac{ 8b - 5c }{ -{3} } = -{3} \cdot \dfrac{ 10b + 9d }{ 2 }$ $8b - 5c = -{3} \cdot \dfrac { 10b + 9d }{ 2 }$ Multiply both sides by the right denominator. $8b - 5c = -3 \cdot \dfrac{ 10b + 9d }{ {2} }$ ${2} \cdot \left( 8b - 5c \right) = {2} \cdot -3 \cdot \dfrac{ 10b + 9d }{ {2} }$ ${2} \cdot \left( 8b - 5c \right) = -3 \cdot \left( 10b + 9d \right)$ Distribute both sides ${2} \cdot \left( 8b - 5c \right) = -{3} \cdot \left( 10b + 9d \right)$ ${16}b - {10}c = -{30}b - {27}d$ Combine $b$ terms on the left. ${16b} - 10c = -{30b} - 27d$ ${46b} - 10c = -27d$ Move the $c$ term to the right. $46b - {10c} = -27d$ $46b = -27d + {10c}$ Isolate $b$ by dividing both sides by its coefficient. ${46}b = -27d + 10c$ $b = \dfrac{ -27d + 10c }{ {46} }$